Application of the Cartier Operator in Coding Theory

2024/01/02 by Nourozi, Vahid · 1 citation
#FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.2401.01305

Abstract

The a-number is an invariant of the isomorphism class of the p-torsion group scheme. We use the Cartier operator on H⁰(A₂,Ω¹) to find a closed formula for the a-number of the form A₂ = v(Y^√(q)+Y-x^{(√(q)+1)/(2)}) where q=p^s over the finite field \mathbbF_q². The application of the computed a-number in coding theory is illustrated by the relationship between the algebraic properties of the curve and the parameters of codes that are supported by it.

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